Diffractive di-jet production at the LHC with a Reggeon contribution

C. Marquet,1, ∗ D.E. Martins,1, 2, † A.V. Pereira,2, ‡ M. Rangel,3, § and C. Royon4, ¶

1Centre de Physique Theorique, Ecole Polytechnique,CNRS, Universite Paris-Saclay, F-91128 Palaiseau, France

2Instituto de Fısica - Universidade do Estado do Rio de Janeiro, Rio de Janeiro 20550-900, RJ, Brazil3Instituto de Fısica - Universidade Federal do Rio de Janeiro, Rio de Janeiro 21941-901, RJ, Brazil

4University of Kansas, Lawrence, KS 66045, USA

We study hard diffractive scattering in hadron-hadron collisions including, on top of the standardPomeron-initiated processes, contributions due to the exchange of Reggeons. Using a simple modelto describe the parton content of the Reggeon, we compute di-jet production in single diffractive andcentral diffractive events. We show that Reggeon contributions can be sizable at the LHC, and evensometimes dominant, and we identify kinematic windows in which they could be experimentallystudied. We argue that suitable measurements must be performed in order to properly constrainthe model, and be able to correctly account for Reggeon exchanges in the analysis of the many harddiffractive observables to be measured at the LHC.

I. INTRODUCTION

Hard diffractive events in hadron-hadron collisions were first observed at the Tevatron [1, 2] more than 20 yearsago, nevertheless the QCD dynamics at play has yet to be understood. In spite of the large transfer of transversemomentum involved in such processes, a satisfactory weak-coupling description remains elusive, and one has to settlefor phenomenological models. To estimate cross-sections of hard processes in single diffractive dissociation (whenone hadron escapes the collision intact) and central diffractive dissociation (when both hadrons escape the collisionintact), a modern version of the resolved-Pomeron model [3] is being widely used.

This model describes hard diffractive scattering in the following way: hadrons scatter through the exchange of acolorless objet called the Pomeron, which carries a longitudinal momentum fraction denoted ξ and a four-momentumsquared denoted t. Then, imitating what happens in collinear factorization, a long-distance/short-distance separationof the Pomeron-induced subprocesses is assumed, into perturbative partonic cross-sections and non-perturbativeparton distribution functions (pdfs) of the Pomeron, that depend on the parton fractional longitudinal momentum β,and on the hard scale of the problem µ2.

The motivation for this model comes from the fact that, in electron-hadron collisions, the diffractive part of thedeep inelastic scattering (DIS) cross-section does obey collinear factorization [4]. The further factorization of thediffractive parton densities fDa/h into a Pomeron flux ΦP/h(ξ, t) and Pomeron parton distributions fa/P(β, µ2) is an

assumption, called Regge factorization, which is accurate and routinely used in QCD fits of diffractive DIS data, fromwhich fq/P, fg/P and ΦP/h are extracted.

When imported to hadron-hadron collisions, such factorization does not apply for diffractive processes, even at verylarge momentum scales, as shown by comparisons to Tevatron data [5]. The presence of additional soft interactionsbetween the colliding hadrons, which may fill the rapidity gap(s), is the standard interpretation of this factorizationbreaking, and there are empirical indications that it can be compensated by an overall factor, called the gap survivalprobability, roughly independent of the details of the hard process. This represents the last ingredient of the resolved-Pomeron model.

At the LHC, a whole new set of experimental studies has started, in order to provide answers to a number ofunsolved questions. Is the gap survival probability only a function of the collision energy, as often assumed? Doesone need a different factor for single diffraction and central diffraction? Is the quark and gluon composition of thePomeron extracted from HERA data compatible with LHC measurements? In this letter, we would like to study adifferent aspect which, to our knowledge, has never been investigated: the possibility that the diffractive scatteringhappens through the exchange of a Reggeon, as opposed to a Pomeron. As a matter of fact, quality fits to diffractiveDIS data do require that both Pomerons and Reggeons contribute to the diffractive pdfs: fDa/h=ΦP/hfa/P+ΦR/hfa/R.

The most important difference between the two contributions resides in the ξ dependence of their fluxes: i.e. theexchange of Reggeons only matters at high ξ, typically for ξ > 0.1.

∗ cyrille.marquet@polytechnique.edu† dan.ernani@gmail.com‡ antonio.vilela.pereira@cern.ch§ murilo.rangel@cern.ch¶ christophe.royon@cern.ch

arX

iv:1

608.

0567

4v1

[he

p-ph

] 1

9 A

ug 2

016

2

⇠1

t1

x1

x2

p

p

p

⇠1

t1

x1

x2

p

p

p

pt2

⇠2

FIG. 1. Leading-order diagrams for di-jet production in single-diffractive events (left) and central-diffractive events (right) inproton-proton collisions. Intact protons can scatter through the exchange of either a Pomeron (P) or a Reggeon (R).

At the LHC, when large diffractive masses are considered - which is the case in a number of studies (see for instance[6]) - such large values are easily reached and one may therefore wonder about the importance of the Reggeoncontribution. That contribution is not always taken into account by standard codes and our goal in this work is toillustrate, within a very simple model where the parton content of the Reggeon is obtained from the pion structurefunction, that indeed the Reggeon contribution cannot be safely neglected, and that for processes where both protonsescape the collision intact, a double-Reggeon exchange can even dominate over a double-Pomeron exchange.

The plan of the letter is as follows. In Section 2, we present more details about the resolved-Pomeron model forhard diffraction in hadron-hadron collisions, we explain its implementation into the Forward Physics Monte Carlo(FPMC) program [7] that we shall utilize, and we outline our subsequent analysis of diffractive di-jets production,the process we have chosen to consider. In Section 3, we present our results, when the Reggeon contribution is turnedon, for both single and central diffractive di-jets. Section 4 is devoted to conclusions and outlook.

II. HARD DIFFRACTIVE PROCESSES WITH REGGEON EXCHANGES

A. Resolved Pomeron model supplemented with Reggeons

The resolved-Pomeron model is a long-distance/short-distance collinear factorization framework commonly usedto calculate hard single-diffractive (SD) and central-diffractive (CD) processes. In this work we focus on di-jetproduction at the LHC. Typical leading-order diagrams for this process are pictured in Fig. 1, and the cross-sectionin the resolved-Pomeron model reads:

dσpp→pJJX = SSD∑a,b

∫fDa/p(ξ1, t1, β1, µ

2)fb/p(x2, µ2) ⊗ dσab→JJX (1)

dσpp→pJJXp = SCD∑a,b

∫fDa/p(ξ1, t1, β1, µ

2)fDb/p(ξ2, t2, β2, µ2) ⊗ dσab→JJX (2)

where dσ is the short-distance partonic cross-section, which can be computed order by order in perturbation theory(provided the transverse momentum of the jets is sufficiently large). fa/p denotes the standard proton parton distri-

butions functions (pdfs) while fDa/p denotes the diffractive ones. These are non-perturbative objects, however their

evolution with the factorization scale µ is perturbative and given by the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi [8]evolution equations (in the following µ is set to the transverse momentum of the leading jet). In Eq. (1) and (2) andin Fig. 1, the variables ξi and ti for the intact protons denote their fractional energy loss and the four-momentumsquared transferred in the collision, respectively. The convolution is done over the longitudinal momentum fractionsof the partons a and b with respect to the incoming protons, namely x1 and x2, respectively. In the case of intactprotons, it is common to use instead βi ≡ xi/ξi, the longitudinal momentum fraction of the parton with respect tothe exchanged Pomeron or Reggeon.

3

Formulae (1) and (2) are reminiscent of the collinear factorization obeyed for inclusive processes. However, itis known that hard diffractive cross-sections in hadronic collisions do not factorize in such a way, due to possiblesecondary soft interactions between the colliding hadrons which can fill the rapidity gaps. In the resolved-Pomeronmodel, the so-called gap survival probabilities SSD and SCD act as corrections to collinear factorization in order toaccount for the effects of the soft interactions. Since those happen on much longer time scales compared to the hardprocess, they are modeled by an overall factor, function of the collision energy only.

B. Pomeron and Reggeon parton-content

In our computations, we shall use the diffractive pdfs fDa/p extracted from HERA data [9] for diffractive DIS, a

process for which collinear factorization does hold. They are obtained by means of a next-to-leading-order QCD fit,in which they are decomposed into Pomeron and Reggeon fluxes ΦP,R/p and their corresponding parton distributionfunctions fa/P,R which depict the partonic structure of the exchanged color singlet objects:

fDa/p(ξ, t, β, µ2) = ΦP/p(ξ, t)fa/P(β, µ2) + ΦR/p(ξ, t)fa/R(β, µ2) with ΦP,R/p(ξ, t) = AP,R

eBP,Rt

ξ2αP,R(t)−1. (3)

The flux normalizations AP,R, the diffractive slopes BP,R, and the Regge trajectories αP,R(t) = αP,R(0) + tα′P,R are

given in Table I for two different fits (known as A and B), and the corresponding Pomeron and Reggeon pdfs fa/P,Rcan be found in the literature.

The Pomeron structure is well constrained by those fits, which clearly show that its parton content is gluondominated. By contrast, the HERA data do not constrain fa/R,but they only indicate that a Reggeon contribution isneeded in order to obtain a quantitative description of the high-ξ measurements. Expectations are that the Reggeoncontribution can be viewed as an exchange of a quark-antiquark pair, hence in those fits fa/R was taken to be the pionstructure function. This led to a quite successful model which we also consider in the following. However one mustkeep in mind this extrapolation to the higher LHC energies is definitely questionable, and it would not be surprisingthat when the LHC will put constraints on fa/R, the model will have to be changed.

The Reggeon contribution is not usually implemented in hard diffraction studies in hadron-hadron collisions, andmeasurements at the LHC will allow to test the validity of this assumption. Indeed, it is often advocated that theReggeon contribution to the diffractive pdfs fDa/p is important only at large values of ξ, at the edge of the Tevatron and

LHC forward proton detector acceptance, or beyond it. Therefore it is routinely disregarded, and subsequently thetheoretical description from (1) and (2) was dubbed the resolved-Pomeron model. But of course it can be supplementedwith resolved Reggeons, and it should be as we will argue below.

Similarly, this is the reason why what we call central diffractive events in this work is usually referred to as double-Pomeron-exchange events in the literature. Since double-Reggeon exchanges or mixtures of Pomeron and Reggeonexchanges are also possible, we choose to use the terminology “central diffractive”. This should not be confusedhowever with central exclusive production which is described by a different production mechanism. The centraldiffractive di-jet final states considered in this work are not exclusive since they contain the so-called Pomeron orReggeon remnants X, that are made of soft particles accompanying the production of the hard di-jet system. Theyreduce the rapidity gaps when compared to the exclusive case, but they do not fill them entirely.

Fits ΦP,R/p α(0) α′ A B

P 1.118± 0.008 0.06+0.19−0.06 GeV−2 * 5.5+0.7

−2.0 GeV−2

AR 0.5± 0.10 0.3−0.3

+0.6 GeV−2 (1.7± 0.4)× 10−3 1.6+0.4−1.6 GeV−2

P 1.111± 0.007 0.06+0.19−0.06 GeV−2 * 5.5+0.7

−2.0 GeV−2

BR 0.5± 0.10 0.3−0.3

+0.6 GeV−2 (1.4± 0.4)× 10−3 1.6+0.4−1.6 GeV−2

TABLE I. Parameters of the Pomeron and Reggeon fluxes. The normalization factor AP is chosen such that ξ ×∫ tmax

tmindt ΦP/p(ξ, t) = 1 at ξ = 0.003, with tmin = −1 GeV2 and tmax = −m2

pξ2/(1−ξ) (mp denotes the proton mass).

4

ξ0 0.05 0.1 0.15 0.2

Events

1

210

410

610

810

ℙp → jjX

ℝp → jjX

ℙp → jjX

ℝp → jjX

­1 = 13 TeV L = 1 pbsFPMC

) > 20 GeV2

, j1

( jT

p

< 0.17ξ

(proton) > 0.15 GeVT

p

ξ0 0.05 0.1 0.15 0.2

Events

1

210

410

610

810

ℙp → jjX

ℝp → jjX

ℙp → jjX

ℝp → jjX

­1 = 13 TeV L = 1 pbsFPMC

) > 50 GeV2

, j1

( jT

p

< 0.17ξ

(proton) > 0.15 GeVT

p

FIG. 2. Number of single diffractive di-jet events as a function of ξ for pT (proton)> 0.15 GeV assuming either a Pomeronexchange (solid lines) or a Reggeon exchange (dashed lines), for pT (j1,2) > 20 GeV (left plot) or pT (j1,2) > 50 GeV (right plot).

C. Hard diffractive di-jet analysis with FPMC

The above theoretical description of hard diffractive processes in hadron-hadron collisions, in which one or bothhadrons remain intact, is implemented by the FPMC generator that we shall employ to perform our analysis. Theparton-level matrix elements are imported from HERWIG [10] routines, while the fit B is adopted for the diffractivepdfs. For proton tagging at the LHC, a region of ξ < 0.17 for both protons is chosen for a center of mass energy of13 TeV, as well as a lower cut of 0.15 GeV for their transverse momenta [11]. In general, the lower boundary for theξ values depends on the minimum mass of the diffractive system, thus related to the jet transverse momenta. For theacceptance we have chosen it is approximately 10−5.

For the di-jets, we apply at generator level a transverse momentum cut on pT >5 GeV, and a pseudo-rapidity cut of|η|<5. The jets are reconstructed using the FastJet [12] package and the anti-kt algorithm, with a value of 0.4 for thejet radius, and a 10 GeV threshold for the transverse momenta. Then, the selection criteria requires at least two jetswith pT larger than 20 GeV, and the two highest transverse momentum jets tagged with pT (j1)>pT (j2). The di-jetmass fraction is defined as RJJ =mJJ/M , i.e. the ratio of the invariant mass of the di-jet system to the invariantmass of the whole diffractive final state, M=

√ξs and M=

√ξ1ξ2s for single and central diffraction, respectively.

Experimentally, the di-jet mass fraction is a good variable for identifying, and for our purpose excluding, possibleexclusive di-jet events. In such events, the di-jet mass is essentially equal to the mass of the central system because noPomeron (or) Reggeon remnants are present, and if the jet definition is such that little is left outside the cones, thenthe presence of an exclusive event would manifest itself as an excess towards RJJ ≈ 1. This observation of exclusiveevents does not depend on the overall normalization of the event distribution, which might be strongly dependent onthe detector simulation and acceptance of the roman pot detectors [13].

Finally, the histograms are normalized according to the relation (σ×L)/Ngen, and our predictions are presented foran integrated luminosity of 1 pb−1 which represents the expected data to be collected in high-β∗ low pile-up runs at theLHC. Note that for the gap survival probabilities, we have assumed for Pomerons and Reggeons SSD = SCD'0.03.There have been several attempts to estimate those probabilities [14–21], but the actual values are rather uncertain,and will be readjusted once the data becomes available. In any case, that does not impact very much our results.

III. NUMERICAL RESULTS FOR THE LHC

A. Single diffractive di-jets

The total cross-sections predicted by FPMC at 13 TeV for single diffractive di-jets assuming either a Pomeronexchange (P + p → jjX) or a Reggeon exchange (R + p → jjX) are 1.51 × 108 pb and 2.3 × 107 pb, respectively.These values assume an acceptance of ξ1 ≡ ξ ≤ 0.17 for the final state intact proton. The ξ distributions are plottedin Figure 2 for two different values of minimum jet pT , 20 or 50 GeV. One clearly sees the dominance of the Pomeronexchange at small ξ (the Reggeon contribution can be neglected for ξ . 0.07), but also the fact that the Reggeoncontribution becomes comparable to it for ξ & 0.1, depending slightly on the jet pT cut.

5

/ MJJ

m

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Ev

en

ts

210

310

410

510

610

710

810

ℙp → jjX

ℝp → jjX

ℙp → jjX

ℝp → jjX

­1 = 13 TeV L = 1 pbsFPMC

) > 20 GeV2

, j1

( jT

p

< 0.17ξ

(proton) > 0.15 GeVT

p

/ MJJ

m

0 0.1 0.2 0.3 0.4 0.5

Even

ts

1

10

210

310

410

510

610

710

810

ℙp → jjX

ℝp → jjX

ℙp → jjX

ℝp → jjX

­1 = 13 TeV L = 1 pbsFPMC

) > 20 GeV2

, j1

( jT

p

< 0.17ξ0.1 <

(proton) > 0.15 GeVT

p

FIG. 3. Di-jet mass fraction distribution in single diffraction assuming either a Pomeron exchange (solid lines) or a Reggeonexchange (dashed lines), for pT (j1,2) > 20 GeV, pT (proton) > 0.15 GeV and for ξ < 0.17 (left) or 0.1 < ξ < 0.17 (right).

This is confirmed by Table II where the number of events are displayed for three different ξ ranges: no minimum ξcut, ξ > 0.015 and ξ > 0.1. In the latter case, the number of events for the Pomeron and Reggeon contributions havethe same order of magnitude. Note that the events for the Pomeron process take into account the uncertainty of theQCD fits at high β: the gluon density fg/P(β,Q2) is multiplied by an uncertainty factor (1−β)ν , with ν = −0.5, 0, or0.5 (the default value in FPMC is ν = 0). The uncertainty range of the Reggeon contribution is not known. Finallythe di-jet mass fraction distributions are displayed in Figure 3, for ξ < 0.17 and 0.1 < ξ < 0.17. While the Reggeonexchange is as important as the Pomeron exchange, there is no kinematical window where it clearly dominates whichwould allow to experimentally isolate it.

Those findings confirm the expectations, that for single diffractive processes sensitive to ξ > 0.1, the Reggeoncontribution should play a non-negligible role. Therefore, the LHC capabilities should be utilized in order to constrainit better, and improve the theoretical predictions of the various high-mass diffractive studies. We will demonstratebelow that central diffractive di-jet production can also be used to constrain the Reggeon contribution even better.

B. Central diffractive di-jets

In central diffraction, besides the double-Pomeron (PP→ jjX) and double-Reggeon (RR→ jjX) exchanges, thereare also cross terms (PR,RP → jjX) which makes the approximation of disregarding the Reggeon contributionseven more questionable. The total cross-sections predicted by FPMC for proton-proton collision at 13 TeV for thosedistinct channels are 1.7× 107 pb (PP), 9.1× 106 pb (PR+RP), and 9.03× 105 pb (RR), again for an acceptance ofξ1,2 ≤ 0.17 for the final state intact protons. These values are in agreement with the prediction that single diffractivecross-sections should be approximately 10 times greater than in the central diffractive case [22].

The ξ distributions are plotted in Figure 4 for a minimum jet pT of 20 GeV. The Pomeron exchange is still dominantat small values of ξ1,2, albeit by a lesser margin than in the single diffractive case, but now the Reggeon contributionsdominate for large values of proton momentum loss. They become comparable to the Pomeron one for ξ1 ∼ 0.14 whenξ2 is integrated in the whole acceptance (Fig. 4-right panel).

Process P p→ jjX R p→ jjX P p→ jjX R p→ jjX

Acceptance pT (j1, j2) > 20 GeV pT (j1, j2) > 50 GeV

ξ1,2 < 0.17 6.06× 105 [5.85× 105, 6.74× 105] 1.38× 104 2.51× 104 [2.26× 104, 2.86× 104 ] 5450

0.015 < ξ1,2 < 0.17 4.58× 105 [4.53× 105, 5.03× 105] 1.37× 104 1.99× 104 [1.81× 104, 2.32× 104 ] 5419

0.10 < ξ1,2 < 0.17 1.49× 105 [1.46× 105, 1.62× 105] 8.77× 104 6561 [6341, 8827] 3521

TABLE II. Number of single diffractive di-jet events for an integrated luminosity of 1 pb−1, and different kinematical windows.For the Pomeron process, the left values inside the brackets stand for ν = 0.5, whereas the right values stand for ν = −0.5.

6

2ξ1

ξ0 0.05 0.1 0.15 0.2

Events

210

310

410

510

610

ℙℙ → jjX

ℙℝ + ℝℙ + ℝℝ → jjX

ℙℙ → jjX

ℙℝ + ℝℙ + ℝℝ → jjX

­1 = 13 TeV L = 1 pbsFPMC

) > 20 GeV2

, j1

( jT

p

< 0.17ξ

(proton) > 0.15 GeVT

p

1ξ

0 0.05 0.1 0.15 0.2

Events

210

310

410

510

610

ℙℙ → jjX

ℙℝ + ℝℙ + ℝℝ → jjX

ℙℙ → jjX

ℙℝ + ℝℙ + ℝℝ → jjX

­1 = 13 TeV L = 1 pbsFPMC

) > 20 GeV2

, j1

( jT

p

< 0.17ξ

(proton) > 0.15 GeVT

p

FIG. 4. Number of central diffractive di-jet events as function of√ξ1ξ2 (left plot) and ξ1 (right plot) for pT (j1,2) > 20 GeV

and pT (proton) > 0.15 GeV. The solid line stands for the double-Pomeron exchange while the dashed line represents the totalReggeon contribution (R R and R R + P R).

/ MJJ

m

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Ev

en

ts

1

210

410

610

810

ℙℙ → jjX

ℙℝ + ℝℙ + ℝℝ → jjX

ℙℙ → jjX

ℙℝ + ℝℙ + ℝℝ → jjX

­1 = 13 TeV L = 1 pbsFPMC

) > 20 GeV2

, j1

( jT

p

< 0.17ξ

(proton) > 0.15 GeVT

p

/ MJJ

m

0 0.1 0.2 0.3 0.4 0.5

Ev

en

ts

1

10

210

310

410

510

610

ℙℙ → jjX

ℙℝ + ℝℙ + ℝℝ → jjX

ℙℙ → jjX

ℙℝ + ℝℙ + ℝℝ → jjX

­1 = 13 TeV L = 1 pbsFPMC

) > 20 GeV2

, j1

( jT

p

< 0.17ξ0.1 <

(proton) > 0.15 GeVT

p

FIG. 5. Di-jet mass fraction distribution in central diffraction for pT (j1,2) > 20 GeV, pT (proton) > 0.15 GeV and for ξ < 0.17(left plot) or 0.1 < ξ < 0.17 (right plot). The solid line stands for the double-Pomeron exchange while the dashed line representsthe total Reggeon “contamination” from the double-Reggeon exchange and from the Pomeron-Reggeon contribution.

This is confirmed by Table III where the number of events is displayed for the same three different ξ1,2 rangesand two different jet pT cuts considered before. As expected, using a larger minimum jet pT further enhances theimportance of the Reggeon exchange, however in central diffraction the number of events quickly becomes too smalland it may not be efficient to use a value greater than 20 GeV. Finally, the di-jet mass fraction distributions aredisplayed in Figure 5, for ξ1,2<0.17 and 0.1<ξ1,2<0.17.

Process P P→ jjX P R+R P→ jjX R R→ jjX P P→ jjX P R+R P→ jjX R R→ jjX

Acceptance pT (j1, j2) > 20 GeV pT (j1, j2) > 50 GeV

ξ1,2 < 0.17 3.34× 104 [2.88× 104, 4.42× 104] 1.56× 104 [1.41× 104, 1.68× 104] 1610 1489 [1198,1829] 697[594,771] 72

0.015 < ξ1,2 < 0.17 2.19× 104 [1.99× 104, 2.79× 104] 1.26× 104 [1.16× 104, 1.35× 104] 1590 1030 [876,1269] 576 [536,644] 70

0.10 < ξ1,2 < 0.17 2530 [2319,3193] 2802 [2627,2850] 680 120[113,135] 148 [140,174] 35

0.10 < ξ1,2 < 0.17 [?] 544 [499,736] 865 [813,877] 312 20.5 [10,23] 42 [36,52] 30

TABLE III. Number of central diffractive di-jet events for an integrated luminosity of 1 pb−1, and different kinematical windows.For the Pomeron process, the left values inside the brackets stand for ν = 0.5, whereas the right values stand for ν = −0.5.The last line [?] is for pT (proton) > 0.4 GeV, instead of the default value 0.15 GeV.

7

1ξ

0 0.05 0.1 0.15 0.2

Ev

en

ts

1

10

210

310

410

510

610

ℙℙ → jjX

ℙℝ + ℝℙ + ℝℝ → jjX

ℙℙ → jjX

ℙℝ + ℝℙ + ℝℝ → jjX

­1 = 13 TeV L = 1 pbsFPMC

) > 20 GeV2

, j1

( jT

p

< 0.17ξ

(proton) > 0.4 GeVT

p

/ MJJ

m

0 0.1 0.2 0.3 0.4 0.5

Even

ts

1

10

210

310

410

510

610

ℙℙ → jjX

ℙℝ + ℝℙ + ℝℝ → jjX

ℙℙ → jjX

ℙℝ + ℝℙ + ℝℝ → jjX

­1

= 13 TeV L = 1 pbsFPMC

) > 20 GeV2

, j1

( jT

p

< 0.17ξ0.1 <

(proton) > 0.4 GeVT

p

FIG. 6. Number of central diffractive di-jet events as function of ξ1 for ξ2 < 0.17 (left plot) and di-jet mass fractiondistribution for 0.1 < ξ < 0.17 (right plot), with pT (j1,2) > 20 GeV and pT (proton) > 0.4 GeV. Increasing that last cutincreases the sensitivity to the Reggeon contribution.

Finally, in Figure 6 we study the sensitivity of our results with respect to the cut on the proton transverse momen-tum. By choosing an alternative cut of 0.4 GeV, we are able to increase the sensitivity to the Reggeon contribution,such that near the edge of the proton detector acceptance, it becomes clearly dominant. By simply measuring thesedistributions, we should already be able to confirm the presence of the Reggeon contribution.

Our results show that di-jets in central diffractive events (formerly known as double-Pomeron-exchange events) atthe LHC could be used to study the Reggeon contribution to hard diffractive processes, since a kinematic window ofdominance has been identified which could be used experimentally to isolate and constrain it.

IV. CONCLUSIONS

In this letter, we studied hard diffractive processes in hadron-hadron collisions using the resolved-Pomeron model(1) and (2), supplemented with a Reggeon term according to formula (3). Our goal is to verify whether or not thiscontribution can be safely neglected at LHC energies. For the moment, it is routinely ignored when estimating harddiffractive cross-sections in hadron-hadron collisions, even though it is needed for a quantitative description of thediffractive DIS HERA data. The Pomeron structure used in the resolved-Pomeron model is extracted from DIS,therefore a consistency check is in order at the LHC.

To do this, we chose to analyze the diffractive di-jet process at the LHC, assuming an integrated luminosity of 1pb−1. We have assumed a simple model in which the parton content of the Reggeon fa/R(β, µ2) is given by the pionstructure function, but it should be pointed out that the related uncertainties are large since the Reggeon structureat low β and high transverse momentum scales is essentially unknown and unconstrained.

Our calculations have been performed using the Forward Physics Monte Carlo program. In the case of singlediffractive di-jets, our results confirm the expectation that the Reggeon contribution is comparable to the Pomeroncontribution only for ξ & 0.1. But since the acceptance of the LHC forward proton detectors goes up to 0.17, itmust be carefully taken into account when the total diffractive mass squared ξs becomes large, which is the case fora number of final states considered in the literature [6].

In the case of central diffractive di-jet production, we find that Reggeon exchanges contribute much more, andcan almost never be completely ignored, at least in our model. For large values of ξ1,2, but still within the detectoracceptances, processes involving Reggeons even clearly dominate over the double-Pomeron exchange. This shouldallow clean experimental studies in order to constrain the Reggeon parton content better and correct the model.Subsequently, many phenomenological studies of double-Pomeron-exchange events at the LHC, such as [23–25], willhave to be corrected in order to take into account the possibility to exchange Reggeons as well.

8

ACKNOWLEDGMENTS

D.E.M. acknowledges the Brazilian Ministry of Science, Technology and Innovation, CNPQ/CAPES, for financial

support, and the Centre de Physique Theorique of Ecole Polytechnique for hospitality. He also warmly thanks GregorySoyez for explanations about the FastJet implementation and the related technical aspects on this analysis.

[1] S. Abachi et al. [D0 Collaboration], Phys. Rev. Lett. 72 (1994) 2332.[2] F. Abe et al. [CDF Collaboration], Phys. Rev. Lett. 74 (1995) 855.[3] G. Ingelman and P. E. Schlein, Phys. Lett. B 152 (1985) 256.[4] J. C. Collins, Phys. Rev. D 57, 3051 (1998) [Erratum-ibid. D 61, 019902 (2000)].[5] T. Affolder et al. [CDF Collaboration], Phys. Rev. Lett. 84 (2000) 5043.[6] e. N.Cartiglia et al. [LHC Forward Physics Working Group Collaboration], CERN-PH-LPCC-2015-001, SLAC-PUB-16364,

DESY-15-167.[7] M. Boonekamp, A. Dechambre, V. Juranek, O. Kepka, M. Rangel, C. Royon and R. Staszewski, arXiv:1102.2531 [hep-ph].[8] G. Altarelli and G. Parisi, Nucl. Phys. B 126, 298 (1977);

V. N. Gribov and L. N. Lipatov, Sov. J. Nucl. Phys. 15, 438 (1972); Sov. J. Nucl. Phys. 15, 675 (1972);Y. L. Dokshitzer, Sov. Phys. JETP 46, 641 (1977).

[9] A. Aktas et al. [H1 Collaboration], Eur. Phys. J. C 48, 715 (2006).[10] G. Corcella, I. G. Knowles, G. Marchesini, S. Moretti, K. Odagiri, P. Richardson, M. H. Seymour and B. R. Webber,

arXiv:0210213 [hep-ph].[11] M. Trzebinski, Proc. SPIE Int. Soc. Opt. Eng. 9290 (2014) 929026.[12] M. Cacciari, G. P. Salam and G. Soyez, Eur. Phys. J. C 72 (2012) 1896.[13] O. Kepka and C. Royon, Phys. Rev. D 76 (2007) 034012.[14] V. A. Khoze, A. D. Martin and M. G. Ryskin, Eur. Phys. J. C 14 (2000) 525.[15] A. B. Kaidalov, V. A. Khoze, A. D. Martin and M. G. Ryskin, Eur. Phys. J. C 21 (2001) 521.[16] J. Bartels, S. Bondarenko, K. Kutak and L. Motyka, Phys. Rev. D 73 (2006) 093004.[17] E. G. S. Luna, Phys. Lett. B 641 (2006) 171.[18] L. Frankfurt, C. E. Hyde, M. Strikman and C. Weiss, Phys. Rev. D 75 (2007) 054009.[19] E. Gotsman, E. Levin and U. Maor, arXiv:0708.1506 [hep-ph].[20] A. Achilli, R. Hegde, R. M. Godbole, A. Grau, G. Pancheri and Y. Srivastava, Phys. Lett. B 659 (2008) 137.[21] V. A. Khoze, A. D. Martin and M. G. Ryskin, Eur. Phys. J. C 55 (2008) 363.[22] G. Aad et al. [ATLAS Collaboration], Eur. Phys. J. C 72 (2012) 1926.[23] C. Marquet, C. Royon, M. Trzebinski and R. Zlebcık, Phys. Rev. D 87 (2013) no.3, 034010.[24] C. Marquet, C. Royon, M. Saimpert and D. Werder, Phys. Rev. D 88 (2013) no.7, 074029.[25] A. K. Kohara and C. Marquet, Phys. Lett. B 757 (2016) 393.